Experiment10.FringesofequalthicknessNewton's rings is a phenomenon offringes ofequal thickness, in which an interferencepattern is created by the reflection of light between two surfaces-a spherical surfaceand an adjacent touching flat surface. It is found by Isaac Newton during making anastronomical telescope in 1675. The pattern was created by placing a very slightlyconvex curved glass (objective) on an optical flat glass. Early 19th century, ThomasYoung explained this phenomenon with the idea of interference. Currently, the methodoffringes of equal thickness is widely used in scientific research, industrial productionand testing. For example, it can be used to measure the wavelength of monochromaticlight and the curvature radius of lens. On the other side, it can be used to accuratelymeasure the thickness ofthin layer,roughness of optical surface and refractive index ofliquid sample and so on.Experimental objectives(1) Observe carefully the phenomenon and features of Newton's rings, and understandthe theory of Fringes of equal thickness(2) Learn how to measure the curvature radius of lens and thickness of thin layer withthe method of Fringes of equal thickness.(3)Knowtheoperationofused scalemicroscope.ExperimentalinstrumentsScalemicroscope,Sodium lamp,Newton's rings component,Wedge-shapedfilmExperimentalprinciple1.Newton's ringsThe pattern of Newton's rings is precisely examined with the arrangement of Figure 1.Here a lens is placed on an optical flat and illuminated at normal incidence with amonochromatic light. The two pieces of glass make contact only at the center, at otherpoints there is a slight air gap between the two surfaces, increasing with radial distancefrom the center. Light from a monochromatic source (Sodium lamp) shines through the
Experiment 10. Fringes of equal thickness Newton's rings is a phenomenon of fringes of equal thickness, in which an interference pattern is created by the reflection of light between two surfaces—a spherical surface and an adjacent touching flat surface. It is found by Isaac Newton during making an astronomical telescope in 1675. The pattern was created by placing a very slightly convex curved glass (objective) on an optical flat glass. Early 19th century, Thomas Young explained this phenomenon with the idea of interference. Currently, the method of fringes of equal thickness is widely used in scientific research, industrial production and testing. For example, it can be used to measure the wavelength of monochromatic light and the curvature radius of lens. On the other side, it can be used to accurately measure the thickness of thin layer, roughness of optical surface and refractive index of liquid sample and so on. Experimental objectives (1) Observe carefully the phenomenon and features of Newton's rings, and understand the theory of Fringes of equal thickness. (2) Learn how to measure the curvature radius of lens and thickness of thin layer with the method of Fringes of equal thickness. (3) Know the operation of used scale microscope. Experimental instruments Scale microscope, Sodium lamp, Newton's rings component, Wedge-shaped film Experimental principle 1. Newton's rings The pattern of Newton’s rings is precisely examined with the arrangement of Figure 1. Here a lens is placed on an optical flat and illuminated at normal incidence with a monochromatic light. The two pieces of glass make contact only at the center, at other points there is a slight air gap between the two surfaces, increasing with radial distance from the center. Light from a monochromatic source (Sodium lamp) shines through the
top piece and reflects from both the bottom surface of the top piece and the top surfaceof the optical flat, and the two reflected rays combine and superpose.The ray reflectingoffthebottom surfacetravels a longer path.The additional pathlength is equal totwicethe gap between the surfaces (A and B shown in Figure 1). In addition, the ray reflectingoffthe bottom piece of glassundergoes a 18oophase reversal because theopticalmedium difference.For illumination from above, the optical path difference k isdetermined by0k= 2ndk +(1-1)where n is the refractive index of air (about I), is the wavelength of the light, anddk is thethickness ofgapatthekth bright-ringMonochromatic lightR-ArBFigure 1.Schematic of Newton'srings componentIf the two pieces of glass are in good contact (no dust),the interference is in accordwith the relationship2k. k=1,2,3... brightrings8k=2dk+(1-2)(2k + 1)=, k = 0,1,2,..dark ringsWithRas theradius of curvatureoftheplano-convex lens, therelationbetween theringradius rk and the film thickness dk is given byrk2 = R2 - (R - dk)2(1-3)or more simply byrk? = 2Rd - dk?(1-4)Since R >> d
top piece and reflects from both the bottom surface of the top piece and the top surface of the optical flat, and the two reflected rays combine and superpose. The ray reflecting off the bottom surface travels a longer path. The additional path length is equal to twice the gap between the surfaces (A and B shown in Figure 1). In addition, the ray reflecting off the bottom piece of glass undergoes a 180° phase reversal because the optical medium difference. For illumination from above, the optical path difference 𝛿𝑘 is determined by 𝛿𝑘 = 2𝑛𝑑𝑘 + 𝜆 2 (1-1) where 𝑛 is the refractive index of air (about 1), 𝜆 is the wavelength of the light, and 𝑑𝑘 is the thickness of gap at the kth bright-ring. Figure 1. Schematic of Newton's rings component If the two pieces of glass are in good contact (no dust), the interference is in accord with the relationship 𝛿𝑘 = 2𝑑𝑘 + 𝜆 2 = { 2𝑘 𝜆 2 ，𝑘 = 1, 2, 3, . bright rings (2𝑘 + 1) 𝜆 2 , 𝑘 = 0,1, 2, . dark rings (1-2) With R as the radius of curvature of the plano-convex lens, the relation between the ring radius rk and the film thickness dk is given by 𝑟𝑘 2 = 𝑅 2 − (𝑅 − 𝑑𝑘) 2 (1-3) or more simply by 𝑟𝑘 2 = 2𝑅𝑑 − 𝑑𝑘 2 (1-4) Since R >> d
rk? = 2Rdk =kRa, k=0,1,2,... dark rings(1-5)It is shown that rs is proportional to the square root of dk.In order to reduce the influenceof disturbed background-noise, the dark rings should be used in our experiments.Due to the pressure deformation, the contact area between the two pieces of glass willturn to be a circle. Sometimes dusts on the glass surface will also change the path length.In fact, with these additional path length, the center of Newton's rings will be a dark orbright circle, which make the measurements of rk very difficultThe differential method is introduced to remove these additional path lengths in ourexperiments.You can writeEq. (1-5)asDm2-Dn2R=(1-6)4(m-n)awhereDm and Dn are the diameters of themth-order and nth-order dark rings,respectively.This method is simpler and more effective without confirmingk.DmFigure2PictureofNewton'srings
𝑟𝑘 2 = 2𝑅𝑑𝑘 = 𝑘𝑅𝜆, k=0,1,2, . dark rings (1-5) It is shown that rk is proportional to the square root of dk. In order to reduce the influence of disturbed background-noise, the dark rings should be used in our experiments. Due to the pressure deformation, the contact area between the two pieces of glass will turn to be a circle. Sometimes dusts on the glass surface will also change the path length. In fact, with these additional path length, the center of Newton's rings will be a dark or bright circle, which make the measurements of 𝑟𝑘 very difficult. The differential method is introduced to remove these additional path lengths in our experiments. You can write Eq. (1-5) as 𝑅 = 𝐷𝑚 2−𝐷𝑛 2 4(𝑚−𝑛)𝜆 (1-6) where Dm and Dn are the diameters of the mth-order and nth-order dark rings, respectively. This method is simpler and more effective without confirming k. Figure 2 Picture of Newton's rings Dn Dm
BEFigure3.Schematicofexperimentalopticalpath2. Fringes from a wedge-shaped filmTwo pieces of plateglass separated at one end by a sheet (or a filament) to form asatisfactory wedge-shape air film as shown in Figure 4. Similar to Newton's ringsexperiment, the monochromatic light shines through the top piece and reflects fromboth the bottom surface A of the top piece and the top surface B of the optical flat, andthe two reflected rays combine and superpose to form the fringes of equal thickness.Each fringe is the locus of all points in the film with the constant optical thickness.Fringes caused by a wedge-film are bands parallel to the contact line between twopieces of plate glass. The bright and dark bands are equispaced. The optical pathdifferencekofdarkbandisdeterminedby8x=2dk+=(2k+1)2k=0,1,2,..The thickness of air film corresponding to the center of kth order dark fringe can bewrittenas1dk=k2when k is O, the dk is O corresponding to the contact position of two plate glass. If aNth order dark fringe can be measured at the position ofthe inserted sheet (or a filament),the thickness of the inserted sheet (or the diameter of the filament) is given by1d=N2Because N is too large to count, we measure the thickness I of several (n) fringes tosimplify measurements. Since N=n·L/l, the thickness d of the inserted sheet (or thediameter of the filament) may be written as
Figure 3. Schematic of experimental optical path. 2. Fringes from a wedge-shaped film Two pieces of plate glass separated at one end by a sheet (or a filament) to form a satisfactory wedge-shape air film as shown in Figure 4. Similar to Newton's rings experiment, the monochromatic light shines through the top piece and reflects from both the bottom surface A of the top piece and the top surface B of the optical flat, and the two reflected rays combine and superpose to form the fringes of equal thickness. Each fringe is the locus of all points in the film with the constant optical thickness. Fringes caused by a wedge-film are bands parallel to the contact line between two pieces of plate glass. The bright and dark bands are equispaced. The optical path difference 𝛿𝑘 of dark band is determined by 𝛿𝑘 = 2𝑑𝑘 + 𝜆 2 = (2𝑘 + 1) 𝜆 2 , k = 0, 1, 2, . The thickness of air film corresponding to the center of kth order dark fringe can be written as 𝑑𝑘 = 𝑘 𝜆 2 when k is 0, the 𝑑𝑘 is 0 corresponding to the contact position of two plate glass. If a Nth order dark fringe can be measured at the position of the inserted sheet (or a filament), the thickness of the inserted sheet (or the diameter of the filament) is given by 𝑑 = 𝑁 𝜆 2 Because N is too large to count, we measure the thickness l of several (n) fringes to simplify measurements. Since N=n•L/l, the thickness d of the inserted sheet (or the diameter of the filament) may be written as
andk=27where L is the distance from the contact position of two plate glass to the position ofthe inserted sheetqFigure 4. Schematic of Fringes from a wedge-shaped filmExperimentalcontentandprocedure1.Measurementofdiameterof Newton's rings(1) Turn on the sodium lamp and preheat it.(2)Align optical path.The beam of monochromatic light was directed normal to thesurfaceof Newton's rings component by 45°mirror of the scale microscope to makefield ofviewbright.(3) Adjust the three screws of Newton's rings component until a perfect interferencepattern in the center, which could be seen by the naked eyes. After adjustment, put theNewton's rings component on the objective table and below the center of objective ofthe scale microscope.(4) Focus the microscope. Focus the ocular lens and objective until there is a clearinterference pattern.(5) Carefully move the Newton's rings component to ensure that the crossing point ofcrosshair is on the center of the interference pattern. Fix the Newton's rings component.(6)Observe the interference pattern.(7) Measure the diameter of Newton's rings from 6th-order to 15th-order dark rings.Rotate wheel of scale microscope to move measurement point in one direction to reduceerrors
𝑑𝑘 = 𝜆 2 𝑛 𝑙 𝐿 where L is the distance from the contact position of two plate glass to the position of the inserted sheet. Figure 4. Schematic of Fringes from a wedge-shaped film. Experimental content and procedure 1. Measurement of diameter of Newton's rings (1) Turn on the sodium lamp and preheat it. (2) Align optical path. The beam of monochromatic light was directed normal to the surface of Newton's rings component by 45o mirror of the scale microscope to make field of view bright. (3) Adjust the three screws of Newton's rings component until a perfect interference pattern in the center, which could be seen by the naked eyes. After adjustment, put the Newton's rings component on the objective table and below the center of objective of the scale microscope. (4) Focus the microscope. Focus the ocular lens and objective until there is a clear interference pattern. (5) Carefully move the Newton's rings component to ensure that the crossing point of crosshair is on the center of the interference pattern. Fix the Newton's rings component. (6) Observe the interference pattern. (7) Measure the diameter of Newton's rings from 6th-order to 15th-order dark rings. Rotate wheel of scale microscope to move measurement point in one direction to reduce errors
1. Measurement of diameter of copper wire with fringes from a wedge-shaped film.()Put the wedge components on the objective table,which is formed with two piecesof plate glass separated at one end by a copper wire. Align the optical path to a clearinterference pattern. The fringes should be parallel to the contact line between twopieces of plate glass.(2) Rotate the wedge components synchronously to make the fringes parallel to one lineof crosshair.(3) Measure the distance / of 10 pairs of fringes.(4) Measure the value of L.Cautions(l) Don't touch the surface of optical components, such as Newton's ringscomponents, lens, wedge components and so on. Clean the surface of opticalcomponents with lens paper.(2)Rotate wheel of scale microscope to move measurement point in one direction(3)Focus the objective from down to the up for protecting it.(4)Avoid measurements in an area surrounded by vibrations of shock(5)Don't screwed the Newton's rings component too tightExperimental data recording and processing(1)Tabulation and record experiment data(2) Calculate the radius of curvature of the plano-convex lens (R)(3)Calculatethediameterofcopperwire (d)Questions(1) Is there any influence if the center of the Newton's rings is a bright circle?(2) How to adjust the Newton's rings component to reduce system error?(3) What will make thefield view of ocular lens unbright? How to solve this problem?
1. Measurement of diameter of copper wire with fringes from a wedge-shaped film. (1) Put the wedge components on the objective table, which is formed with two pieces of plate glass separated at one end by a copper wire. Align the optical path to a clear interference pattern. The fringes should be parallel to the contact line between two pieces of plate glass. (2) Rotate the wedge components synchronously to make the fringes parallel to one line of crosshair. (3) Measure the distance l of 10 pairs of fringes. (4) Measure the value of L. Cautions (1) Don’t touch the surface of optical components, such as Newton's rings components, lens, wedge components and so on. Clean the surface of optical components with lens paper. (2) Rotate wheel of scale microscope to move measurement point in one direction. (3) Focus the objective from down to the up for protecting it. (4) Avoid measurements in an area surrounded by vibrations of shock. (5) Don’t screwed the Newton's rings component too tight. Experimental data recording and processing (1) Tabulation and record experiment data. (2) Calculate the radius of curvature of the plano-convex lens (R). (3) Calculate the diameter of copper wire (d). Questions (1) Is there any influence if the center of the Newton's rings is a bright circle? (2) How to adjust the Newton's rings component to reduce system error? (3) What will make the field view of ocular lens unbright? How to solve this problem?